### Some articles on *turing degrees, turing, turing degree, degree, degrees*:

Structure of The

... A great deal of research has been conducted into the structure of the

**Turing Degrees**... A great deal of research has been conducted into the structure of the

**Turing degrees**... that can be drawn from the research is that the structure of the**Turing degrees**is extremely complicated ...Recursion Theory - Areas of Research - Relative Computability and The

... traditionally focused on relative computability, a generalization of

**Turing Degrees**... traditionally focused on relative computability, a generalization of

**Turing**computability defined using oracle**Turing**machines, introduced by**Turing**(1939) ... An oracle**Turing**machine is a hypothetical device which, in addition to performing the actions of a regular**Turing**machine, is able to ask questions of an oracle, which is a particular set of natural ... If a set A is**Turing**reducible to a set B and B is**Turing**reducible to A then the sets are said to have the same**Turing degree**(also called**degree**of ...Recursion Theory - Areas of Research - Automorphism Problems

... sets, automorphisms are also studied for the structure of the

... sets, automorphisms are also studied for the structure of the

**Turing degrees**of all sets as well as for the structure of the**Turing degrees**of r.e ... In both cases, Cooper claims to have constructed nontrivial automorphisms which map some**degrees**to other**degrees**this construction has, however, not been verified and some colleagues believe that the ...Theodore Slaman

... Hugh Woodin formulated the Bi-interpretability Conjecture for the

... Hugh Woodin formulated the Bi-interpretability Conjecture for the

**Turing degrees**, which conjectures that the partial order of the**Turing degrees**is logically equivalent to second ... is equivalent to there being no nontrivial automorphism of the**Turing degrees**... They also exhibited limits on the possible automorphisms of the**Turing degrees**by showing that any automorphism will be arithmetically definable ...### Famous quotes containing the word degrees:

“Always the laws of light are the same, but the modes and *degrees* of seeing vary.”

—Henry David Thoreau (1817–1862)